Apparatus and methods for providing efficient space-time structures for preambles, pilots and data for multi-input, multi-output communications systems

ABSTRACT

Apparatus and methods for providing efficient space-time structures for preambles, pilots and data for multi-input, multi-output (MIMO) communications systems are provided. One such embodiment includes providing a computer program that includes logic configured to provide an initial structure. The computer program further includes logic configured to verify that the rows of the initial structure are linearly independent and logic configured to apply an orthonormalization procedure to the initial structure to obtain a space-time structure. Methods are also provided for providing efficient space-time structures for preambles, pilots and data for MIMO communications systems.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to co-pending U.S. provisionalapplication entitled, “Efficient Training and Synchronization SequenceStructures for MIMO OFDM,” having serial No. 60/322,786, filed Sep. 17,2001, which is entirely incorporated herein by reference.

This application is related to co-pending U.S. provisional applicationentitled “Preamble Structures for SISO and MIMO OFDM Systems,” havingSer. No. 60/327,145, filed on Oct. 4, 2001, which is entirelyincorporated herein by reference.

TECHNICAL FIELD OF THE INVENTION

The present invention is generally related to communications systemsand, more particularly, to Multi-Input, Multi-Output (MIMO)communications systems.

BACKGROUND OF THE INVENTION

Significant developments in communications have been made by theintroduction of technologies that increase system operating efficiency(i.e., system “throughput”). One example of these technologies is theuse of two or more transmit antennas and two or more receive antennas(i.e., multiple antennas) in a wireless communications system thatemploys multiple frequencies (i.e., multiple carriers). Such systems aretypically referred to as Multi-Input, Multi-Output (MIMO) communicationssystems. In contrast, traditional wireless communications systemstypically employ one transmit antenna and one receive antenna operatingat a single signal-carrier frequency (SC), and such systems are referredto accordingly as Single-Input, Single-Output (SISO) systems.

In the operation of MIMO communications systems, signals are typicallytransmitted over a common path (i.e., a channel) by multiple antennas.The signals are typically pre-processed to avoid interference from othersignals in the common channel. There are several techniques that may beused to pre-process the signals in this regard, and some of thesetechniques may be combined to further improve system throughput. Onesuch technique, known as Space-Time Processing (STP), processes andcombines “preambles” and “data symbols” into “space-time signalstructures.” Wireless communications systems typically transmit data orinformation (e.g., voice, video, audio, text, etc.) as formattedsignals, known as data symbols (or information symbols), which aretypically organized into groups, known as data frames (or informationframes).

Training symbols (or preamble symbols) are another type of symbol, whichare typically added as prefixes to data symbols (e.g., at the beginningof data frames), to enable training (i.e., synchronization) of the datasymbols between the transmitters and receivers of a MIMO communicationssystem. These training symbol prefixes can be referred to as preamblesor preamble structures. The combination of the preambles and datasymbols can be referred to as space-time signal structures. Space-timestructures may also be constructed using STP for preambles and datasymbols individually. Furthermore, pilot structures (or pilots) arespace-time structures that are also constructed by STP and have the samestructure as preambles, although they are periodically arranged withingroups of data symbols for different purposes. Certain propertiesincorporated into space-time signal structures make it possible torecover the data symbols from them through post-processing by areceiver, for example. Moreover, the formation and processing ofspace-time signal structures in a wireless communications system mayprovide increased strength (i.e., gain) in the recovered signal, whichtypically enhances the performance of the communications system.

Another technique that may be used to pre-process signals in MIMOcommunications systems is called Frequency Division Multiplexing (FDM).FDM involves dividing the frequency spectrum of a wirelesscommunications system into sub-channels and transmitting modulated dataor information (i.e., formatted signals for voice, video, audio, text,etc.) over these sub-channels at multiple signal-carrier frequencies(“sub-carrier frequencies”). Orthogonal Frequency Division Multiplexing(OFDM) has emerged as a popular form of FDM in which the sub-carrierfrequencies are spaced apart by precise frequency differences. Theapplication of OFDM technologies in SISO communications systems (i.e.,SISO OFDM systems) provides the capability, among others, to transmitand receive relatively large amounts of information. The application ofOFDM in MIMO communications systems (i.e., MIMO OFDM systems) providesthe added capability of increased capacity to transmit and receiveinformation using, generally, the same amount of bandwidth (i.e.,transmission line capacity) as used in SISO OFDM systems. MIMO OFDMcommunications systems also offer improved performance to overcome someof the difficulties experienced in other FDM communications systems,such as performance degradation due to multiple versions of atransmitted signal being received over various transmission paths (i.e.,multi-path channel interference).

In wireless communications systems (e.g., SISO or MIMO), synchronizationof data symbols is typically required in both time and frequency.Estimation of noise variance and channel parameters is also typicallyrequired. Thus, efficient preamble structures and pilot structures foruse in wireless communications systems should provide bothsynchronization and parameter estimation. Furthermore, efficientpreamble structures and pilot structures should possess a lowpeak-to-average power ratio (PAPR) (i.e., at or approaching unity) tofacilitate efficient system operation. In their application to MIMOcommunications systems, however, existing preamble structures and pilotstructures have shortcomings in their capability to provide theforegoing functions of time and frequency synchronization, estimation ofnoise variance and channel parameters, and low PAPR. For example, theIEEE Standard 802.11a preamble structure includes a short sequence,which provides time synchronization and coarse frequency offsetestimation, followed by a long sequence, which provides fine frequencyand channel estimation. Although this preamble has direct application toSISO communications systems, it is not directly applicable to MIMOcommunications systems to provide the above mentioned functions, withoutthe need for significant modifications.

Existing techniques for space-time processing of preamble symbols, pilotsymbols, and data symbols into space-time structures also haveshortcomings in their applications to MIMO communications systems. Forexample, existing space-time structures (i.e., preamble, pilot, or data)are typically limited to applications in MIMO communications systemsthat employ two, four, or eight transmit antennas. However, MIMOcommunications systems may be required that employ other numbers oftransmit antennas to satisfy various applications. As another example,existing space-time structures do not support the “full diversity”performance of MIMO communications systems. That is, existing space-timestructures do not support the optimal signal transmission performancethat MIMO communications systems can provide. For example, a MIMOcommunications system that employs four transmit antennas can provide afull diversity signal transmission performance of four space-timestructures over four time periods. However, typical existing space-timestructures are limited to support a signal transmission performance ofno better than three space-time structures over four time periods in afour-antenna MIMO system.

Therefore, there is a need for apparatus and methods for providingefficient preamble structures and pilot structures that provide time andfrequency synchronization, estimation of noise variance and channelparameters, and low PAPR in their application to MIMO communicationssystems. Moreover, there is a need for an apparatus and methods forproviding space-time structures (i.e., preamble, pilot, or data) thatcan be applied to MIMO communications systems with any number oftransmit and receive antennas and that facilitate full diversityperformance of MIMO communications systems.

SUMMARY OF THE INVENTION

The present invention provides an apparatus and methods for providingefficient space-time structures for preambles, pilots and data formulti-input, multi-output (MIMO) communications systems.

Briefly described, one embodiment of the present invention, amongothers, includes providing a computer program that includes logicconfigured to provide an initial structure. The computer program furtherincludes logic configured to verify that the rows of the initialstructure are linearly independent and logic configured to apply anorthonormalization procedure to the initial structure to obtain aspace-time structure.

The present invention can also be viewed as providing methods forproviding efficient space-time structures for preambles, pilots and datafor MIMO communications systems. In this regard, one embodiment of sucha method, among others, can be broadly summarized by the following:providing an initial structure, verifying that the rows of the initialstructure are linearly independent, and applying an orthonormalizationprocedure to the initial structure to obtain a space-time structure.

Another embodiment of a method of the present invention can be broadlydescribed by the following: selecting a data structure, verifying thatthe data structure is a unitary transmission matrix, and applying thedata structure as a space-time preamble structure.

Other apparatus, methods, features and advantages of the presentinvention will be or become apparent to one with skill in the art uponexamination of the following drawings and detailed description. It isintended that all such additional apparatus, methods, features, andadvantages be included within this description, be within the scope ofthe present invention, and be protected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the invention can be better understood with reference tothe following drawings. Moreover, in the drawings, like referencenumerals designate corresponding parts throughout the several views.

FIG. 1 is a block diagram of an exemplary Multi-Input, Multi-Output(MIMO) communications system.

FIG. 2 is a block diagram of an exemplary encoder with respect to thecommunications system depicted in FIG. 1.

FIG. 3 is a diagram illustrating exemplary signal transmissions andassociated signal sample matrices with respect to the communicationssystem depicted in FIG. 1.

FIG. 4 is a graphical illustration of a version of the receive samplematrix shown in FIG. 3 that is applicable to the MIMO communicationssystem of FIG. 1 when employing Orthogonal Frequency DivisionMultiplexing (OFDM).

FIG. 5 illustrates an exemplary frame that may be implemented in theMIMO communications system depicted in FIG. 1.

FIG. 6 is a flow chart illustrating a method for providing efficientspace-time structures for preambles, pilots and data that may beimplemented in the MIMO communications system depicted in FIG. 1.

FIG. 7 is a flow chart illustrating an exemplary method to determine aninitial structure for use in the method described with respect to FIG.6.

FIG. 8 is a flow chart illustrating an alternative method for providingefficient space-time structures for preambles, pilots and data that maybe implemented in a MIMO communications system, such as the systemdepicted in FIG. 1.

DETAILED DESCRIPTION

The invention now will be described more fully with reference to theaccompanying drawings. The invention may, however, be embodied in manydifferent forms and should not be construed as limited to theembodiments set forth herein; rather, these embodiments are intended toconvey the scope of the invention to those skilled in the art.Furthermore, all “examples” given herein are intended to benon-limiting.

FIG. 1 shows a block diagram of an exemplary Multi-Input, Multi-Output(MIMO) communications system 6. The exemplary MIMO communications system6 and its sub-components will be described hereinafter to facilitate thedescription of the present invention. In that regard, the exemplary MIMOcommunications system 6 may be implemented as a wireless system for thetransmission and reception of data across a wireless channel 19, asdepicted in FIG. 1. For example, the MIMO communications system 6 may beimplemented as part of a wireless Local Area Network (LAN) orMetropolitan Area Network (MAN) system, a cellular telephone system, oranother type of radio or microwave frequency system incorporatingone-way or two-way communications over a range of distances.

The MIMO communications system 6 may transmit and receive signals atvarious frequencies. For example, the MIMO communications system 6 maytransmit and receive signals in a frequency range from 2 to 11 GHz, suchas in the unlicensed 5.8 GHz band, using a bandwidth of about 3 to 6MHz. Further, the MIMO communications system 6 may employ various signalmodulation and demodulation techniques, such as Single-Carrier FrequencyDomain Equalization (SCFDE) or Orthogonal Frequency DivisionMultiplexing (OFDM), for example. However, throughout this description,references may be made with respect to a MIMO OFDM communicationssystems merely to facilitate the description of the invention.

The MIMO communications system 6 may also be implemented as part of acommunications system (not shown) that includes an array of sub-channelcommunications links, which convey one or more signals transmitted byone or more transmitting elements to one or more receiving elements. Thesub-channel communications links may include wires (e.g., in a wiringharness) or other forms of tangible transmission medium that spanbetween a data source and a receiver within the communications system.

The MIMO communications system 6 includes a transmitter 8 and a receiver10. The transmitter 8 typically transmits signals across a channel 19 tothe receiver 10. As depicted in FIG. 1, the transmitter 8 typicallyincludes several components. In this regard, the transmitter 8 includesan encoder 14. The encoder 14 typically encodes data and/or other typesof signals received, for example, from a data source 12. Such signalsmay alternatively be referred to collectively hereinafter as “data,”“signals,” or “data signals.” The data source 12 may be a device,system, etc. that outputs such signals. The encoder 14 may also performfunctions such as employing a channel code on data for transmission andforming sequence structures by space-time processing (STP) techniques.Further, the encoder 14 may separate the received signals onto one ormore signal paths 15, included in the transmitter 8, which will bereferred to hereinafter as transmit diversity branches (TDBs) 15. EachTDB 15 may correlate to a different sub-channel within the MIMOcommunications system 6. The encoder 14 typically facilitates thetransmission of signals across the channel 19 by bundling the signalsinto groups, which are typically referred to as a “frame.” Details of aframe, with respect to the present invention, will be discussed furtherbelow.

The transmitter 8 also includes one or more modulators 16 that areconfigured to modulate signals for transmission over the channel 19. Inthis regard, the modulators 16 may employ various modulation techniques,such as SCFDE or OFDM. The modulators 16 are typically connected to theencoder 14 by the TDBs 15. The transmitter also includes one or moretransmit antennas 18 connected respectively to the one or moremodulators 16. Thus, each TDB 15 directs signals from the encoder 14 toone or more modulators 16, and the modulators 16 modulate the signalsfor transmission by a respective transmit antenna 18.

As discussed above, the exemplary MIMO communications system 6, shown inFIG. 1, also includes a receiver 10. The receiver 10 also typicallyincludes several components. The receiver includes one or more receiveantennas 20 that are connected to one or more demodulators 22,respectively. The receive antennas 20 typically receive modulatedsignals that are transmitted across the channel 19 from the transmitantennas 18. The received signals are typically directed to thedemodulators 22 from the respective receive antennas 20. Thedemodulators 22 demodulate signals that are received by the respectivereceive antennas 20.

The receiver 10 also includes a decoder 24, which is connected to thedemodulators 22. The decoder 24 typically combines and decodesdemodulated signals from the demodulators 22. In this regard, thedecoder 24 typically recovers the original signals that were input tothe transmitter 8 from the data source 12 and transmitted across thechannel 19. As depicted in FIG. 1, the original signals recovered by thedecoder 24 may be transmitted to a connected data sink 25, which mayinclude one or more devices configured to utilize or process theoriginal signals.

As discussed above, the transmitter 8 of the MIMO communications system6 includes one or more modulators 16 that are connected to one or moretransmit antennas 18, respectively. Further, the receiver 10 of thecommunications system 6 includes one or more demodulators 22 that areconnected to one or more receive antennas 20, respectively. In thisregard, the number of modulators 16 and respective transmit antennas 18that are implemented in the transmitter 8 may be represented by a firstvariable, “Q.” Similarly, the number of demodulators 22 and respectivereceive antennas 20 that are implemented in the receiver 10 may berepresented by a second variable, “L.” In the exemplary MIMOcommunications system 6, the number (Q) of modulators 16 and respectivetransmit antennas 18 may be equivalent or non-equivalent to the number(L) of demodulators 22 and respective receive antennas 20. In thisregard, the communications system 6 may be said to have “Q×L”transmit-receive diversity.

FIG. 2 is a block diagram of an exemplary encoder 14 with respect to thecommunications system 6 depicted in FIG. 1. The elements of the encoder14 shown in FIG. 2 will be described below with respect to severalelements that were described above for FIG. 1. The exemplary encoder 14includes a channel encoder 26. The channel encoder 26 typically convertsdata and/or other types of signals to channel encoded versions of thesignals, which may also be referred to collectively as “channel encodeddata” or “channel encoded signals.” These signals may be received by thechannel encoder 26 from a data source 12, for example. The channelencoder 26 is typically configured to encode signals using an encodingscheme that can be recognized by the decoder 24 of the receiver 10 thatis intended to receive the channel encoded signals. In the process ofencoding signals, the channel encoder 26 also typically adds parity tothe signals so that the receiving decoder 24 can detect errors in thereceived channel encoded signals, which may occur, for example, due toenvironmental conditions of the channel 19 or inadvertent noiseinjection by the transmitter 8 or receiver 10, for example.

The exemplary encoder 14 depicted in FIG. 2 also includes a symbolmapper 28, which receives channel encoded data from the channel encoder26. The symbol mapper 28 is typically configured to map channel encodeddata into data symbols. The symbol mapper 28 typically maps channelencoded data into data symbols by grouping a predetermined number ofbits of the data so that each group of bits constitutes a specificsymbol that is selected from a pre-determined symbol alphabet. In thisregard, a symbol alphabet typically includes a finite set of values. Forexample, a symbol alphabet of a binary phase shift keying (BPSK) systemtypically consists of the values +1 and −1, and a symbol alphabet for aquadrature phase shift keying (QPSK) system typically consists of thevalues 1+j, −1+j, 1−j, and −1−j. The symbol mapper 28 is also typicallyconfigured to structure a stream of data symbols into a data section,which will be discussed further below.

The exemplary encoder 14 also includes a space-time processor 30. Thespace-time processor 30 is typically configured to encode data symbolstreams (i.e., data sections), received from the symbol mapper 28,through space-time processing to form space-time structures withproperties that enhance the performance of the communication systems 6.The encoded data sections are output from the space-time processor 30over Q lines 13, where Q represents the number of modulators 16 andrespective transmit antennas 18 of the transmitter 8, as discussedabove.

As illustrated in FIG. 2, the Q output lines from the space-timeprocessor 30 input respectively to Q adders 34. The encoder 14 alsoincludes a pilot/training symbol inserter 32, which also has Q outputlines 17 that input respectively to the Q adders 34. As depicted in FIG.2, the Q adders 34 output to Q transmit diversity branches (TDBs) 15,which input respectively to Q modulators 16. The pilot/training symbolinserter 32 typically provides pilot symbols and training symbols thatare inserted into (or combined with) data sections by the adders 34,which then output the modified data sections as space-time structuresover the TDBs 15.

The term pilot symbols, as used in this description, refers to symbolsprovided by the pilot/training symbol inserter 32, which are insertedperiodically into data sections. Typically, pilot symbols may beinserted at any point in a data section. The term training symbols, asalso used in this description, refers to one or more continuous sectionsof training symbols provided by the pilot/training symbol inserter 32,which are inserted into data sections. Training symbols are preferablyinserted into data sections at the beginning of the section andtransmitted once per frame. However, training symbols may also beinserted at other parts of data sections, such as the middle or end ofthe sections. Preambles (or preamble structures) are symbol structuresformed of training symbols. Pilot structures (or pilots) are symbolstructures formed of pilot symbols.

Pilot symbols are typically transmitted with data sections to performminor adjustments to the calibration (i.e., synchronization and channelparameter estimation) of the receiver 10 to the transmitter 8 toaccommodate, for example, the time varying nature of the channel 19.Training symbols, however, are typically used for periodic calibrationof the receiver 10 to the transmitter 8. The training symbols that aretransmitted for each sub-channel may be unique. Moreover, different setsof training symbols and/or pilot symbols may be provided by thepilot/training symbol inserter 32, depending on the operating criteriaof the communications system 6, which may be determined, for example, bythe user. However, although pilot symbols and training symbols havedifferent purposes, the structure of preambles and pilot structures arethe same. Therefore, all descriptions made hereinafter, in accordancewith the present invention, with respect to preambles or preamblesstructures also apply to pilots or pilot structures unless otherwisespecified).

FIG. 3 is a diagram that illustrates exemplary signal transmissions andassociated signal sample matrices with respect to themodulator/demodulator configuration of the communications system 6depicted in FIG. 1. As shown in FIG. 3, the configuration includes oneor more modulators 16 and one or more demodulators 22. As discussedabove with respect to FIG. 1, the modulators 16 and the demodulators 22may be configured to modulate and demodulate signals, respectively, byvarious techniques, such as SCFDE or OFDM.

Each modulator 16 is connected to one or more respective transmitantennas 18, and each demodulator 22 is connected to one or morerespective receive antennas 20. As discussed above with respect to FIG.1, the transmit antennas 18 are typically configured to transmitmodulated signals across a channel 19, and the receive antennas 20 aretypically configured to receive modulated signals via the channel 19. Inthis regard, exemplary signal transmissions are depicted in FIG. 3,which will be discussed further below.

Similar to the above discussion with respect to the MIMO communicationssystem 6 of FIG. 1, in the modulator/demodulator configuration of FIG.3, the number of modulators 16 and respective transmit antennas 18 thatare implemented may be represented by the variable, “Q.” Accordingly,the number of demodulators 22 and respective receive antennas 20 in thearrangement of FIG. 3 may be represented by the variable, “L.” Thus themodulator/demodulator arrangement depicted in FIG. 3 may also bedescribed as having “Q×L” transmit-receive diversity. Moreover, thevariables, Q and L, may be equivalent or non-equivalent in variousconfigurations of the modulators 16 and demodulators 22.

Exemplary signal transmissions from the Q transmit antennas 18 to the Lreceive antennas 20, across the channel 19, are also depicted in FIG. 3.For example, a first of the L receive antennas 20 may receive each ofthe Q transmitted signals from the Q transmit antennas 18. These Qtransmitted signals are typically transmitted over channel impulseresponses h₁₁, h₂₁, h₃₁, . . . , h_(Q1), that are transmitted from the1^(st) to the Q^(th) transmit antennas 18, respectively, as depicted inFIG. 3. In this regard, the term h_(ij) (where i=1, 2, 3, . . . , Q andj=1, 2, 3, . . . , L) is used to refer to the channel impulse response,in the time domain, that is transmitted from the i^(th) transmit antenna18 to the j^(th) receive antenna 20. Thus, as a further example, theL^(th) receive antenna 20 may receive each of the Q transmitted signals,over the channel impulse responses h_(1L), h_(2L), h_(3L), . . . ,h_(QL), from the 1^(st) to the Q^(th) transmit antennas 18,respectively, as depicted in FIG. 3. Although, for simplicity, exemplarysignal transmissions are depicted in FIG. 3 from the Q transmit antennas18 to only the 1^(st) and the L^(th) receive antennas 20, in a typicalMIMO communications system, signals transmissions may occur from any ofthe Q transmit antennas 18 to any of the L receive antennas 20.

A transmit sample matrix S is illustrated in FIG. 3. The matrix S isassociated with the signals that are modulated by the Q modulators 16and transmitted over the channel 19 from the Q transmit antennas 18. Inthis regard, the sample matrix S may be associated with signals that aretransmitted by a MIMO communications system. Thus, the elements of thetransmit sample matrix S may represent Q space-time symbols (i.e.,preamble or data), which are simultaneously transmitted from the Qtransmit antennas 18 during Q or more symbol periods (“T_(S)”). Forexample, the elements of the first row of the transmit sample matrix Smay represent the symbols S₁, S₂, . . . , S_(Q), which are transmittedfrom the 1^(st) through the Q^(th) transmit antennas 18, respectively,at a first time (“t”). Similarly, the elements of the second row of thetransmit sample matrix S may represent the symbols S_(Q+1), S_(Q+2), . .. , S_(2Q), which are transmitted from the 1^(st) through the Q^(th)transmit antennas 18, respectively, at a second time (“t+T_(S)”). Theelements of the last row of the transmit sample matrix S may representthe final set of symbols, S_((Q−1)Q+1), S_((Q−1)Q+2), . . , S_(QQ),which are transmitted from the 1^(st) through the Q^(th) transmitantennas 18, respectively, at a final time (“t+(Q−1)T_(S)”).

Also illustrated in FIG. 3 is a receive sample matrix R, which isassociated with the signals that are received over the channel 19 by theL receive antennas 20 and demodulated by the L demodulators 22. Similarto the elements of the transmit sample matrix S, described above, theelements of the receive sample matrix R may represent L space-timesymbols, which are simultaneously received by the L receive antennas 20during Q or more symbol periods (“T_(S)”). For example, the elements ofthe first row of the receive sample matrix R may represent the symbolsR₁, R_(Q+1), . . . , R_((L−1)Q+1), which are demodulated by the 1^(st)through the L^(th) demodulators 22, respectively, at a first time (“t”).Similarly, the elements of the second row of the receive sample matrix Rmay represent the symbols R₂, R_(Q+2) . . . , R_((L−1)Q+2), which aredemodulated by the 1^(st) through the L^(th) demodulators 22,respectively, at a second time (“t+T_(S)”). The elements of the last rowof the receive sample matrix R may represent the final set of symbols,R_(Q), R_(2Q), . . . , R_(QL), which are demodulated by the 1^(st)through the L^(th) demodulators 22, respectively, at a final time(“t+(Q−1)T_(S)”). It is noted that although references are made to thesame time instances (e.g., t, t+T_(S), etc.) in the foregoingdescriptions, as well as in FIG. 3, with respect to the transmit samplematrix S and the receive sample matrix R, there is typically a timedelay between the transmission and reception of the signals representedby these matrices.

In addition to the transmit sample matrix S and the receive samplematrix R, there are at least two other matrices that are relevant torepresent the transmission and reception of signals in a MIMOcommunications system, such as the system depicted in FIGS. 1 and 3. Thechannel matrix η typically includes elements that represent channelcoefficients, which are determined based on characteristics of thechannel 19. The channel matrix η typically has a dimension of Q×L. Thenoise matrix W typically includes elements that represent additive whiteGaussian noise, which typically causes distortion and corruption ofreceived signals that are represented, for example, by the receivesample matrix R. The noise matrix W typically has a dimension of Q×L.

The relationship between the receive sample matrix R, the transmitsample matrix S, the channel matrix η, and the noise matrix W can beexpressed by the following equation:R _(k,T×L) =S _(k,T×Q)·η_(k,Q×L) +W _(k,T×L)  EQ. 1With respect to EQ. 1, k represents the sub-carrier or sub-channel ofreceived demodulated signals and T represents a dimension variable thatis typically equivalent to Q, although it may have other values. Asdiscussed above, Q and L represent, respectively, the number ofmodulators 16 and respective transmit antennas 18 and the number ofdemodulators 22 and respective receive antennas 20 with respect to atypical MIMO communications system 6.

FIG. 4 is a graphic illustration of a version of the receive samplematrix R′ shown in FIG. 3 that is applicable to the MIMO communicationssystem of FIG. 1, when employing Orthogonal Frequency DivisionMultiplexing (OFDM). As shown, the x axis represents space, the y axisrepresents time, and the z axis represents frequency. Each receivesample matrix R_(k) that is depicted in the space-time dimensions issimilar to the receive sample matrix R discussed above with respect toFIG. 3. However, each element of the receive sample matrix R′illustrated in FIG. 4 also has N frequency components that are eachrepresented by an index, “k”. As k varies from 0 to N−1 for the elementsof each receive sample matrix R_(k) in FIG. 4, the frequency componentof the received symbol varies accordingly. Thus, the three-dimensionalreceive sample matrix R′ can be viewed as including N receive samplematrices R_(k) of dimensions Q×L or Q*L vectors R_(1,j) of length N. Forexample, with respect to the symbol received by the 1^(st) antenna anddemodulated by the 1^(st) demodulator, there is a vector of elementsR_(1,0), R_(1,1), . . . , R_(1,N−1), as depicted in FIG. 4.

FIG. 5 illustrates an exemplary frame 50 that may be implemented in aMIMO communications system that has Q transmit antennas, such as thecommunications system depicted in FIGS. 1 and 3. As depicted in FIG. 5,the frame 50 typically includes Q signal structures 52, which correspondrespectively to the Q antennas. Each signal structure 52 typicallyincludes a preamble 54 and a data section 56. As discussed above forFIG. 2, the preamble 54 is typically inserted into the data section 56by the pilot/training symbol inserter 32. The preamble 54 typicallyincludes one or more training blocks 58 of length N_(I) and cyclicprefixes 57 of length G, as depicted in FIG. 5. The combination of acyclic prefix 57 and a training block 58 forms a training symbol 53 thathas a length of G+N_(I) samples in the time domain. Thus, as depicted,the preamble 54 typically includes Q training symbols 53 that have anoverall length of Q*(G+N_(I)) samples in the time domain. A cyclicprefix 57 may also be referred to as a guard interval, since the cyclicprefix 57 typically functions to guard the signal structures 52 frominter-symbol interference (ISI) during transmission as a frame 50 acrossthe channel 19. The time length of the cyclic prefix 57 is typicallygreater than the maximum length of the channel impulse response h_(ij),which was discussed above for FIG. 3.

As also depicted in FIG. 5, the data section 56 typically includes oneor more data blocks 59 of length N and cyclic prefixes 57 of length G.The combination of a cyclic prefix 57 and a data block 59 forms a datasymbol 55 that has a length of G+N samples in the time domain.Therefore, the data section 56 of the signal structure 52 typicallyincludes Q or more data symbols 55 that have an overall length ofP*Q*(G+N) samples in the time domain, as depicted in FIG. 5, where P issome positive integer. Although not depicted in FIG. 5, for simplicity,pilot symbols may also be intermittently inserted into the data symbols55 by the pilot/training symbol inserter 32, as discussed above.

The length N_(I) of a training block 58 may be shorter than the length Nof a data block 59 in a signal structure 52. Typically, the length N_(I)of a training block 58 in the preamble 54 is established as a fractionof the length N of a data block 59 in the data section 56 to provide therelationship of N_(I) being equivalent to N/I, where I is some positiveinteger. For example, N_(I) may be equivalent to N/4 (i.e., I=4). If thelength N_(I) of a training block 58 is not established, the length N_(I)may be assumed to be equivalent to N (i.e., I=1). Typically, the lengthof a training symbol 53 (i.e., G+N_(I)) is equivalent to the length of adata symbol 55 (i.e., G+N). However, it is feasible for the trainingsymbol 53 to be shorter than the data symbol 55 in the context of thesignal structure 52.

A primary purpose of the preamble 54 is to enable the receiver 10(FIG. 1) to identify the arrival of the signal structure 52. Thus, thepreamble 54 may facilitate time synchronization, frequencysynchronization, channel parameter estimation, and noise varianceestimation. Efficient space-time structures for the preamble 54(“space-time preamble structures”), in accordance with the presentinvention, provide time synchronization, frequency synchronization,channel parameter estimation, and noise variance estimation throughsynchronization signals that have low peak-to-average power ratios(PAPR) (e.g., at or approaching unity).

A space-time preamble structure, which may also be referred to as aspace-time training structure, may be represented by a signaltransmission matrix S_(k). In accordance with an embodiment of thepresent invention, the signal transmission matrix S_(k) of an efficientspace-time preamble structure should be a unitary transmission matrix inthe frequency domain and have a low PAPR in the time domain. In thisregard, efficient space-time preamble structures provide enhancedperformance in MIMO communications systems.

A unitary transmission matrix contains rows and columns that areorthogonal to each other, and the energy of the signals represented byeach row or column is unity. In mathematical terms, a unitarytransmission matrix has the properties represented by the followingequations:

$\begin{matrix}{{\sum\limits_{j = 1}^{Q}{S_{i,j}S_{i^{\prime},j}^{*}}} = \left\{ \begin{matrix}1 & {i = i^{\prime}} \\0 & {i \neq i^{\prime}}\end{matrix} \right.} & \text{EQ.~~2A} \\{{\sum\limits_{i = 1}^{Q}{S_{i,j}S_{i,j^{\prime}}^{*}}} = \left\{ \begin{matrix}1 & {j = j^{\prime}} \\0 & {j \neq j^{\prime}}\end{matrix} \right.} & \text{EQ.~~2B}\end{matrix}$where S_(i,j) represents the constituent symbols of the unitarytransmission matrix.

Providing a space-time preamble structure that is a unitary signaltransmission matrix S_(k) reduces or eliminates noise enhancement duringchannel estimation of the received signals. Moreover, providing aspace-time preamble structure that possesses a low PAPR reduces oreliminates signal non-linearities and spurious, out-of-band signaltransmissions. As will be discussed below, data structures formed byspace-time processing (i.e., space-time data structures) to be a unitarytransmission matrix also provide enhanced performance in MIMOcommunications systems.

The following descriptions present several examples of data structuresthat, in accordance with the present invention, can be applied and/ormodified to provide space-time preamble structures that are unitarytransmission matrices. As a first example, a diagonal data structure canbe applied and/or modified to provide a space-time preamble structure inaccordance with the present invention. In this regard, the resultingdiagonal space-time preamble structure is a unitary transmission matrix.The following diagonal structure S_(D1) is an example of this unitarytransmission matrix that can be applied as a space-time preamble in aMIMO communications system with Q antennas:

$\begin{matrix}{S_{D} = \begin{bmatrix}S_{1} & 0 & \cdots & 0 \\0 & S_{2} & \cdots & \vdots \\\vdots & 0 & ⋰ & 0 \\0 & \cdots & 0 & S_{Q}\end{bmatrix}} & \text{EQ.~~3}\end{matrix}$

The foregoing diagonal space-time preamble structure S_(D1) can besimplified so that the same training symbol (e.g., S₁) can betransmitted from each antenna, instead of Q different training symbols(i.e., S₁, S₂, etc.), as shown by the following simplified diagonalstructure S_(DS) that can be applied, in accordance with the presentinvention, as a space-time preamble structure in a MIMO communicationssystem with Q antennas:

$\begin{matrix}{S_{DS} = \begin{bmatrix}S_{1} & 0 & \cdots & 0 \\0 & S_{1} & \cdots & \vdots \\\vdots & 0 & ⋰ & 0 \\0 & \cdots & 0 & S_{1}\end{bmatrix}} & \text{EQ.~~4}\end{matrix}$

When the foregoing diagonal structures S_(D), S_(DS) are applied asspace-time preamble structures in a MIMO communications system, thetraining symbols are transmitted sequentially in time from eachcorresponding transmit antenna, and the parameters of the receivedsymbols are estimated by the receivers connected to each receiveantenna. Due to their unitary characteristic, the diagonal structuresS_(D), S_(DS), provide simplified signal acquisition (i.e.,synchronization) and parameter estimation when applied as a space-timepreamble structure in a MIMO communications system. These diagonalstructures S_(D), S_(DS), are preferably applied as space-time preamblestructures, in MIMO communications systems that use two transmitantennas. As the number (Q) of transmit antennas in the MIMO system isincreased, the power output from each transmit antenna typically has tobe reduced by a factor of Q due to the nature of MIMO systems. As aresult, the efficiency of the diagonal space-time preamble structuresS_(D), S_(DS) may decrease in MIMO systems with more than two transmitantennas, since the diagonal structures S_(D), S_(DS) only includesymbols on the main diagonal (i.e., spanning from the top-left to thebottom).

A data structure that was introduced by S. Alamouti is another exampleof a data structure that can be applied and/or modified, in accordancewith the present invention, to provide a space-time preamble structureS_(A). This data structure is a unitary transmission matrix, and it canbe applied as a space-time preamble structure S_(A), in MIMOcommunications systems that employ two transmit antennas. The space-timepreamble structure S_(A) has the following form:

$\begin{matrix}{S_{A} = \begin{bmatrix}S_{1} & S_{2} \\{- S_{2}^{*}} & S_{1}^{*}\end{bmatrix}} & \text{EQ.~~5}\end{matrix}$

In the above space-time preamble structure S_(A), the “*” symbolindicates a complex conjugate operation. The foregoing space-timepreamble structure S_(A) can also be simplified, in accordance with thepresent invention, so that the same training symbol is transmitted fromeach of the two antennas of the MIMO system, as shown by the followingsimplified space-time preamble structure S_(AS):

$\begin{matrix}{S_{AS} = \begin{bmatrix}S_{1} & S_{1} \\{- S_{1}^{*}} & S_{1}^{*}\end{bmatrix}} & \text{EQ.~~6}\end{matrix}$

Several orthogonal structures that were introduced by V. Tarokh, et al.are examples of data structures that can be applied and/or modified, inaccordance with the present invention, to provide space-time preamblestructures that are unitary transmission matrices. These data structurescan be applied as space-time preamble structures, in accordance with thepresent invention, in MIMO communications systems that employ four oreight transmit antennas. For a four-antenna MIMO system, the followingspace-time preamble structure S_(T4) can be applied, in accordance withpresent invention, when the constituent symbols have real number values:

$\begin{matrix}{S_{T4} = \begin{bmatrix}S_{1} & S_{2} & S_{3} & S_{4} \\{- S_{2}} & S_{1} & {- S_{4}} & S_{3} \\{- S_{3}} & S_{4} & S_{1} & {- S_{2}} \\{- S_{4}} & {- S_{3}} & S_{2} & S_{1}\end{bmatrix}} & \text{EQ.~~7}\end{matrix}$The foregoing space-time preamble structure S_(T4) can be simplified, inaccordance with the present invention, so that the same training symbolis transmitted from each of the four antennas of the MIMO system, asshown by the following simplified space-time preamble structure S_(T4S).The symbols of this structure S_(T4S) may have complex values (e.g.,W+jX):

$\begin{matrix}{S_{T4S} = \begin{bmatrix}S_{1} & S_{1} & S_{1} & S_{1} \\{- S_{1}} & S_{1} & {- S_{1}} & S_{1} \\{- S_{1}} & S_{1} & S_{1} & {- S_{1}} \\{- S_{1}} & {- S_{1}} & S_{1} & S_{1}\end{bmatrix}} & \text{EQ.~~8}\end{matrix}$

The foregoing simplified structures S_(AS), S_(T4S) (i.e., EQ. 6 and EQ.8) typically form unitary transmission matrices when applied asspace-time preamble structures, without further modification.Furthermore, the PAPR of the simplified space-time preamble structuresS_(AS), S_(T4S) are typically unity when the symbols consist ofchirp-type sequences, such as:

$\begin{matrix}{\left. {{s_{n} = {\exp\left( \frac{j\;\pi\; n^{2}}{N} \right)}},{n = 0},1,\ldots\mspace{11mu},{N - 1}} \right).} & \text{EQ.~~9}\end{matrix}$Therefore, these simplified structures S_(AS), S_(T4S) are typicallyefficient (i.e., they provide time and frequency synchronization,estimation of noise variance and channel parameters, and low PAPR) whenapplied, in accordance with the present invention, as space-timepreamble structures.

The foregoing structures S_(A), S_(T4) (i.e., EQ. 5 and EQ. 7) are alsotypically efficient when applied as space-time preamble structures, inaccordance with the present invention. The structure S_(T4) is typicallynot efficient when applied as space-time data structures in a MIMOcommunications system. However, both structures S_(A), S_(T4) can bemodified and then applied as efficient space-time data structures, inaccordance with the present invention. Since the structures S_(A),S_(T4) will include symbols with complex values when they are applied asspace-time data structures, the resultant data structures will typicallynot be unitary transmission matrices. Therefore, the structures S_(A),S_(T4) can be modified, in accordance with the present invention, toform unitary transmission matrices and, thus, provide efficientspace-time data structures. Methods, in accordance with the presentinvention, to transform these structures S_(A), S_(T4) and otherstructures into efficient space-time data structures will be describedbelow.

The following space-time preamble structure S_(T8) is based on anotherdata structure by Tarokh, et al., and the structure S_(T8) can beapplied in eight-antenna MIMO communications systems, in accordance withpresent invention, when the constituent symbols have real number values:

$\begin{matrix}{S_{T8} = \left\lbrack \begin{matrix}S_{1} & S_{2} & S_{3} & S_{4} & S_{5} & S_{6} & S_{7} & S_{8} \\{- S_{2}} & S_{1} & S_{4} & {- S_{3}} & S_{6} & {- S_{5}} & {- S_{8}} & S_{7} \\{- S_{3}} & {- S_{4}} & S_{1} & S_{2} & S_{7} & S_{8} & {- S_{5}} & {- S_{6}} \\{- S_{4}} & S_{3} & {- S_{2}} & S_{1} & S_{8} & {- S_{7}} & S_{6} & {- S_{5}} \\{- S_{5}} & {- S_{6}} & {- S_{7}} & {- S_{8}} & S_{1} & S_{2} & S_{3} & S_{4} \\{- S_{6}} & S_{5} & {- S_{8}} & S_{7} & {- S_{2}} & S_{1} & {- S_{4}} & S_{3} \\{- S_{7}} & S_{8} & S_{5} & {- S_{6}} & {- S_{3}} & S_{4} & S_{1} & {- S_{2}} \\{- S_{8}} & {- S_{7}} & S_{6} & S_{5} & {- S_{4}} & {- S_{3}} & S_{2} & S_{1}\end{matrix} \right\rbrack} & \text{EQ.~~10}\end{matrix}$

The foregoing space-time preamble structure S_(T8) can be simplified, inaccordance with the present invention, so that the same training symbolis transmitted from each of the eight antennas of the MIMO system, asshown by the following simplified space-time preamble structure S_(T8S)

$\begin{matrix}{{S_{T8S} = \begin{bmatrix}S_{1} & S_{1} & S_{1} & S_{1} & S_{1} & S_{1} & S_{1} & S_{1} \\{- S_{1}} & S_{1} & S_{1} & {- S_{1}} & S_{1} & {- S_{1}} & {- S_{1}} & S_{1} \\{- S_{1}} & {- S_{1}} & S_{1} & S_{1} & S_{1} & S_{1} & {- S_{1}} & {- S_{1}} \\{- S_{1}} & S_{1} & {- S_{1}} & S_{1} & S_{1} & {- S_{1}} & S_{1} & {- S_{1}} \\{- S_{1}} & {- S_{1}} & {- S_{1}} & {- S_{1}} & S_{1} & S_{1} & S_{1} & S_{1} \\{- S_{1}} & S_{1} & {- S_{1}} & S_{1} & {- S_{1}} & S_{1} & {- S_{1}} & S_{1} \\{- S_{1}} & S_{1} & S_{1} & {- S_{1}} & {- S_{1}} & S_{1} & S_{1} & {- S_{1}} \\{- S_{1}} & {- S_{1}} & S_{1} & S_{1} & {- S_{1}} & {- S_{1}} & S_{1} & S_{1}\end{bmatrix}}} & \text{EQ.~~11}\end{matrix}$

The foregoing structures S_(T8), S_(T8S) (i.e., EQ. 10 and EQ. 11) aretypically efficient when applied as space-time preamble structures, inaccordance with the present invention. However, these structures S_(T8),S_(T8S) are typically not efficient when applied as space-time datastructures in a MIMO communications system. The structure S_(T8)preferably can be modified and then applied as efficient space-time datastructures, in accordance with he present invention. Since the structureS_(T8) will include symbols with complex values when it is applied as aspace-time data structure, the resultant data structure will typicallynot be a unitary transmission matrix. Therefore, the structure S_(T8)can be modified, in accordance with the present invention, to form aunitary transmission matrix and, thus, provide an efficient space-timedata structure. Methods, in accordance with the present invention, totransform this structure S_(T8) and other structures into efficientspace-time data structures will be described below.

Orthogonal structures, such as those introduced by Tarokh, et al.,typically only have applications to MIMO communications systems thatemploy two, four, or eight transmit antennas. As described above, someof the orthogonal structures can be applied, in accordance with thepresent invention, in two-antenna MIMO systems as space-time datastructures, with complex symbols, that are unitary transmissionmatrices. However, the application of existing orthogonal structuresusing complex symbols (e.g., for space-time data structures) in MIMOsystems having more than two transmit antennas typically results in aloss of the system diversity gain and/or system bandwidth. For example,the following orthogonal structure S_(T3) was introduced by Tarokh, etal. for use as a data structure with complex symbols in a three-antennaMIMO system:

$\begin{matrix}{S_{T3} = \begin{bmatrix}S_{1} & S_{2} & \frac{S_{3}}{\sqrt{2}} \\{- S_{2}^{*}} & S_{1}^{*} & \frac{S_{3}}{\sqrt{2}} \\\frac{S_{3}^{*}}{\sqrt{2}} & \frac{S_{3}^{*}}{\sqrt{2}} & \frac{{- S_{1}} - S_{1}^{*} + S_{2} - S_{2}^{*}}{2} \\\frac{S_{3}^{*}}{\sqrt{2}} & \frac{S_{3}^{*}}{\sqrt{2}} & \frac{S_{2} + S_{2}^{*} + S_{1} - S_{1}^{*}}{2}\end{bmatrix}} & \text{EQ.~~12}\end{matrix}$

When the foregoing structure S_(T3) is applied in a three-antenna MIMOsystem, it does not provide the full diversity performance of thesystem, which is the capability to transmit three symbols over threesymbol periods. Instead, the structure S_(T3) only provides for thetransmission of three symbols over four symbol periods, which isapparent since the structure has a four rows instead of three. This lackof full diversity may result in a loss of as much as 25% of systemthroughput. However, methods, in accordance with the present invention,will be discussed below to transform such inefficient structures intoefficient space-time structures (for preambles or data) that providefull diversity performance in MIMO communications systems.

The foregoing space-time preamble structures, in accordance with thepresent invention, can be applied in a Q-antenna MIMO communicationssystem, such as the system 6 depicted in FIG. 1, using any applicabletechnique. For example, the space-time preamble structure S_(T4) may bestored in a pilot/training symbol inserter 32 of the transmitter 8 of afour-antenna MIMO communications system 6 and combined with one or moredata symbols for transmission over a channel 19, as discussed above.

In general the transmission matrix for Q transmit antennas over Q symbolintervals can be represented by the following matrix S_(Q) ²:

$\begin{matrix}{S_{Q^{2}} = \begin{bmatrix}S_{1} & S_{2} & \cdots & S_{Q} \\S_{Q + 1} & S_{Q + 2} & \cdots & S_{2Q} \\\vdots & \; & \; & \vdots \\S_{{Q{({Q - 1})}} + 1} & \cdots & \cdots & S_{Q^{2}}\end{bmatrix}} & \text{EQ.~~13}\end{matrix}$This general transmission matrix S_(Q) ² can be composed using Q²different symbols (or sequences in the case of OFDM modulation).However, in general, only Q sequences are used to form a structure. Asdiscussed above, the transmission performance of Q symbols over Q symbolperiods indicates full diversity performance of the MIMO system and alsoindicates the utilization of the full bandwidth of the system. Thus,such performance indicates the optimal use of the system resources.

In order to utilize the structure of the foregoing general transmissionmatrix S_(Q) ² to construct efficient space-time sequence structures forpreambles, pilots and data to be applied in MIMO communications systems,the matrix S_(Q) ² is pre-processed and/or pre-conditioned in accordancewith the present invention.

FIG. 6 is a flow chart illustrating a method 120 for providing efficientspace-time structures for preambles, pilots and data that may beimplemented in a MIMO communications system, such as the system 6depicted in FIG. 1. The method 120 begins with a step 122 in which oneor more initial structures S_(in) are provided for conversion intoefficient space-time structures for preambles or data. The structureS_(in) will typically have a form that is applicable to a Q×L MIMOcommunications system, where Q represents the number of transmitantennas and L represents the number of receive antennas, as discussedabove. Thus, if the initial structure S_(in) is to be applied to a MIMOsystem that has 4 transmit antennas (i.e., Q=4), the structure willtypically have 4 columns and 4 rows, similar to the general transmissionmatrix S_(Q) ² described above. Typically, the initial structure S_(in)is formed of symbols from a known symbol alphabet. As discussed above, asymbol alphabet typically includes a finite set of values. In general,the initial structure S_(in) may be any structure that has a possibleapplication to a MIMO communications system with Q transmit antennas.One method, among others, to determine an initial structure S_(in) willbe discussed below with respect to FIG. 7.

Following step 122, the method 120 proceeds to step 124 in which therows of the initial structure S_(in) are verified to be linearlyindependent. The check for linear independence of the rows of theinitial structure S_(in) may be performed by various methods andtechniques, which may be known in the art. For example, the rows of theinitial structure S_(in) can be tested for linear independence bydetermining the rank of the initial structure S_(in). If the rank of theinitial structure S_(in) is determined to be Q, the rows of the initialstructure S_(in) are linearly independent. If the rows of the initialstructure S_(in) are determined to be linearly independent, the method120 proceeds to the next step 126. However, if the rows of the initialstructure S_(in) are determined not to be linearly independent, themethod 120 returns to step 122, in which one or more different initialstructures S_(in) are provided and the method 120 proceeds again to step124.

In the step 126, an orthonormalization (i.e., orthogonalization andnormalization) procedure is applied to the initial structure S_(in). Theorthonormalization procedure may be any procedure that transforms theinitial structure S_(in) to a space-time structure S_(out) that has theproperties of a unitary signal transmission matrix. As discussed above,a unitary transmission matrix has the following mathematical properties:

$\begin{matrix}{{\sum\limits_{j = 1}^{Q}{S_{i,j}S_{i^{\prime},j}^{*}}} = \left\{ \begin{matrix}1 & {i = i^{\prime}} \\0 & {i \neq i^{\prime}}\end{matrix} \right.} & \text{EQ.~~2A} \\{{\sum\limits_{i = 1}^{Q}{S_{i,j}S_{i,j^{\prime}}^{*}}} = \left\{ \begin{matrix}1 & {j = j^{\prime}} \\0 & {j \neq j^{\prime}}\end{matrix} \right.} & \text{EQ.~~2B}\end{matrix}$where S_(i,j) represents the constituent symbols of the unitarytransmission matrix. One example of an orthonormalization procedure thatmay be applied to the initial structure S_(in) to obtain a space-timestructure S_(out) that is a unitary signal transmission matrix is knownas a row-wise Gram-Schmidt procedure. An example application of arow-wise Gram-Schmidt procedure will be presented below.

The resultant space-time structure S_(out) that is obtained by the step126 may be applied as an efficient space-time preamble structure or anefficient space-time data structure, depending on the characteristics ofthe constituent symbols of the structure. For example, as discussedabove, an efficient space-time preamble structure includes symbols thatprovide time and frequency synchronization and estimation of noisevariance and channel parameters. In contrast, an efficient space-timedata structure typically includes symbols that have complex values, asalso discussed above. Further, if OFDM modulation is employed in thecommunications system, the constituent symbols will be symbol sequences,as also discussed above.

The resultant space-time structure S_(out) may be applied accordingly asa space-time preamble or data structure in a Q-antenna MIMOcommunications system, such as the system 6 depicted in FIG. 1, usingany applicable technique, which may be known in the art. For example, aresultant space-time preamble structure S_(out) may be stored in apilot/training symbol inserter 32 of MIMO communications systemtransmitter 8 and combined with one or more data symbols fortransmission over a channel 19, as discussed above.

FIG. 7 is a flow chart illustrating an exemplary method 140, amongothers, to determine an initial structure S_(in) for use in the step 122described above for FIG. 6. The exemplary method 140 begins with a step142 in which a symbol alphabet is chosen to provide the symbols for theinitial structure S_(in). Preferably, the symbols (or symbol sequencesin the case of OFDM modulation) are derived from a complex alphabet onthe unit circle, that is, all of the alphabet points have the sameenergy. The following are exemplary alphabets in this regard:

-   -   Binary Phase Shift Keying (BPSK) alphabet: +1, −1    -   Quadrature Phase Shift Keying (QPSK) alphabet: 1+j, −1+j, −1−j,        1−j    -   8-Phase Shift Keying (8-PSK) alphabet: exp(j*2πi/8), i=0, 1, 2,        . . . , 7    -   16-Phase Shift Keying (16-PSK) alphabet: exp(j*2πi/16), i=0, 1,        2, . . . , 15    -   32-Phase Shift Keying (32-PSK) alphabet: exp(j*2πi/32), i=0, 1,        2, . . . , 31    -   In general, M-Phase Shift Keying (M-PSK) alphabet: exp(j*2πi/M),        i=0, 1, 2, . . . , M−1; M=8, 16, 32, . . .

The symbols or symbols sequences may also be derived from polyphasesequences, such as Chirp sequences; Milewski sequences; Frank-Zadoffsequences; Chu sequences; Suehiro polyphase sequences; and Ng et al.sequences, among others known in the art.

Following the step 142, the method 140 concludes with a step 144 inwhich the initial configuration of the initial structure S_(in) ischosen. The determination of the initial configuration may add certainspecific characteristics to the structure. For example, the initialconfiguration typically reduces the number of possible symbolcombinations from Q² to Q. The initial configuration may be chosen fromany structure configuration. The following are several examples of apossible initial configuration of the initial structure S_(in):

-   -   Circular configuration, S_(C):

$\begin{matrix}{S_{C} = \begin{bmatrix}S_{1} & S_{2} & \cdots & S_{Q} \\S_{Q} & S_{1} & \cdots & S_{Q - 1} \\\vdots & \; & \; & \vdots \\S_{2} & \cdots & \cdots & S_{1}\end{bmatrix}} & \text{EQ.~~14}\end{matrix}$

-   -   Symmetric configuration, S_(S):

$\begin{matrix}{S_{S} = \begin{bmatrix}S_{1} & S_{2} & \cdots & S_{Q} \\S_{2} & S_{1} & \cdots & S_{Q - 1} \\\vdots & \; & \; & \vdots \\S_{Q} & \cdots & \cdots & S_{1}\end{bmatrix}} & \text{EQ.~~15}\end{matrix}$

Based on the determination of the symbol alphabet and the initialstructure configuration in the step 142 and the step 144, respectively,an initial structure S_(in) can be determined. This initial structureS_(in) can be used in the method 120, depicted in FIG. 6, to obtain anefficient space-time structure, as discussed above.

FIG. 8 is a flow chart illustrating an alternative method 160 forproviding efficient space-time structures for preambles, pilots and datathat may be implemented in a MIMO communications system, such as thesystem 6 depicted in FIG. 1. The method 160 begins with a step 162 inwhich one or more initial structures S_(in) are provided for conversioninto efficient space-time structures for preambles or data. The step 162is at least substantially similar to the step 122 discussed above withrespect to FIG. 6. Following the step 162, the method 160 proceeds to astep 164 in which the rows of the initial structure S_(in) are verifiedto be linearly independent. This step 164 is at least substantiallysimilar to the step 124 discussed above with respect to FIG. 6.

If the rows of the initial structure S_(in) are determined to belinearly independent, the method 160 proceeds from the step 164 to astep 166 in which an orthonormalization procedure is applied to theinitial structure S_(in) to transform the initial structure S_(in) to aspace-time structure S_(out) that has the properties of a unitary signaltransmission matrix. This step 166 is at least substantially similar tothe step 126 discussed above with respect to FIG. 6. However, if therows of the initial structure S_(in) are determined not to be linearlyindependent, the method 160 returns to step 162.

Following the step 166, the method 160 proceeds to a step 168 in whichthe alphabet points of the constituent symbols of the resultantspace-time structure S_(out) are checked to be within a tolerabledistance of the alphabet points of the constituent symbols of theinitial structure S_(in). The amplitude of the alphabet points may bemodified during the orthonormalization procedure in the step 166. Thetolerable distance is typically dependent on the operating capability ofcomponents of the MIMO communications system 6, such asdigital-to-analog (D/A) converters. The constituent symbols of thespace-time structure S_(out) may be checked to be within a tolerabledistance of the original alphabet points by various methods andtechniques, which are known in the art. For example, the constituentsymbols of the space-time structure S_(out) may be checked to be withina tolerable distance by application of a Euclidean distance metricrepresented, for example, by the following equation:d _(t,l) =∥S _(t) −S _(l)∥²  EQ. 16

If the constituent symbols of the space-time structure S_(out) are foundto be within a tolerable distance from the original alphabet points ofthe initial structure S_(in), the space-time structure S_(out) is storedin a memory or other device for application in a MIMO communicationssystem. However, if the constituent symbols of the space-time structureS_(out) are not determined to be within a tolerable distance from theoriginal alphabet points, the method 160 returns to step 162, in whichone or more different initial structures S_(in) are provided and themethod 160 proceeds again as described above.

In the case of a MIMO communications system that employs OFDMmodulation, the steps 162 through 168 may be repeated until a sufficientnumber of space-time structures S_(out) that are unitary signaltransmission matrices are obtained and stored, as discussed above.

If the symbols are within a tolerable distance, in step 170, the storedspace-time structure S_(out) used to construct space-time sequencestructures S_(out,k), where k represents a sub-carrier or sub-channelindex of the OFDM setup. The space-time sequence structures S_(out,k)may be constructed by an encoder, as described above with respect toFIGS. 2 and 5, or other methods, which may be known in the art, may beutilized to construct the space-time sequence structures S_(out,k).

In the final step 172 of the method 160, the peak-to-average power ratio(PAPR) of the space-time sequence structures S_(out,k) are tested todetermine if the PAPR of the structures is low enough to provideefficient signal transmission and reception in a MIMO OFDMcommunications system. The PAPR of the training sequences may be testedby various methods and techniques, which may be known in the art. Forexample, the PAPR of the space-time sequence structures S_(out,k) may betested by converting the structures to the time domain (e.g., by inverseFourier transform or “IFT”) and calculating the PAPR of the resultantsignal samples. If the PAPR of the space-time sequence structuresS_(out,k) is found to be acceptable (e.g., at or approaching unity), thestructures have been determined to be efficient, in accordance with thepresent invention, and may be used for preambles or data in a MIMOcommunications system 6 employing OFDM modulation. However, if the PAPRof the space-time sequence structures S_(out,k) are found to beunacceptably high, the method 160 returns to step 162, in which one ormore different initial structures S_(in) are provided and the method 160proceeds again as described above.

In the case of some orthogonal polyphase sequences, complex coefficientsb_(i) that are used to modulate the sequences may be useful to formefficient space-time sequence structures S_(out,k). In this regard,modulation of the orthogonal polyphase sequences by the complexcoefficients b_(i) may make the rows of the corresponding space-timestructures S_(out) linearly independent. Furthermore, the modulation bythe complex coefficients b_(i) may also reduce the PAPR of the resultingspace-time sequence structures S_(out,k) that are formed from thespace-time structures S_(out).

In the step 126 of the method 120 and the step 166 of the method 160,described above with respect to FIGS. 6 and 8, respectively, anorthonormalization procedure is applied to the initial structure S_(in)to transform the initial structure S_(in) to a space-time structureS_(out) that has the properties of a unitary signal transmission matrix.As discussed above, one example of such an orthonormalization procedureis a row-wise Gram-Schmidt procedure. In general, when a matrix S_(k) issubjected to the Gram-Schmidt procedure, the resulting matrix S′_(k)will be unitary, so long as the rank of S_(k) is Q or the rows of S_(k)are linearly independent. In a row-wise application of the Gram-Schmidtprocedure to a matrix S_(k), the first row of the matrix S_(k) isunchanged and used as a reference to make the remaining rows orthonormal(i.e., orthogonal and normal). The following matrices illustrate theapplication of a row-wise Gram-Schmidt procedure to a 4×4 matrix S_(k)to obtain the orthogonalized unitary matrix S′_(k):

$\begin{matrix}{S_{k} = \begin{bmatrix}{{.5}\;{\mathbb{e}}^{{- {.03}}j}} & {{.5}\;{\mathbb{e}}^{{.00}j}} & {{.5}\;{\mathbb{e}}^{{.00}j}} & {{.5}\;{\mathbb{e}}^{{.07}j}} \\{{.5}\;{\mathbb{e}}^{{- {.89}}j}} & {{.5}\;{\mathbb{e}}^{{- {.49}}j}} & {{.5}\;{\mathbb{e}}^{{.17}j}} & {{.5}\;{\mathbb{e}}^{{- {.32}}j}} \\{{.5}\;{\mathbb{e}}^{{- {.69}}j}} & {{.5}\;{\mathbb{e}}^{{- {.80}}j}} & {{.5}\;{\mathbb{e}}^{{.20}j}} & {{.5}\;{\mathbb{e}}^{{- {.28}}j}} \\{{.5}\;{\mathbb{e}}^{{- 1.3}j}} & {{.5}\;{\mathbb{e}}^{{- {.72}}j}} & {{.5}\;{\mathbb{e}}^{{- {.70}}j}} & {{.5}\;{\mathbb{e}}^{{- {.74}}j}}\end{bmatrix}} & \text{EQ.~~17} \\{S_{k}^{\prime} = \begin{bmatrix}{{.5}\;{\mathbb{e}}^{{- {.03}}j}} & {{.5}\;{\mathbb{e}}^{{.00}j}} & {{.5}\;{\mathbb{e}}^{{.00}j}} & {{.5}\;{\mathbb{e}}^{{.07}j}} \\{{.62}\;{\mathbb{e}}^{{- 2.0}j}} & {{.16}\;{\mathbb{e}}^{{- 1.4}j}} & {{.76}\;{\mathbb{e}}^{1.3j}} & {{.1}\;{\mathbb{e}}^{{- {.2}}j}} \\{{.47}\;{\mathbb{e}}^{{- {.75}}j}} & {{.83}\;{\mathbb{e}}^{{- 2.2}j}} & {{.24}\;{\mathbb{e}}^{1.3j}} & {{.14}\;{\mathbb{e}}^{{- 1.0}j}} \\{{.37}\;{\mathbb{e}}^{{- 2.6}j}} & {{.17}\;{\mathbb{e}}^{{- 2.4}j}} & {{.34}\;{\mathbb{e}}^{{- {.70}}j}} & {{.85}\;{\mathbb{e}}^{{- {.88}}j}}\end{bmatrix}} & \text{EQ.~~18}\end{matrix}$

It is noted that embodiments of the present invention, such as thosedescribed above, may be implemented in hardware, software, firmware, ora combination thereof. For example, in some embodiments, the presentinvention may be implemented as a computer program or application insoftware or firmware that is stored in a memory and that is executed bya suitable instruction execution system. In other embodiments thepresent invention may be implemented, for example, with one or acombination of the following technologies, which may be known in theart: one or more discrete logic circuit(s) having logic gates forimplementing logic functions upon data signals, an application specificintegrated circuit (ASIC) having appropriate combinational logic gates,a programmable gate array(s) (PGA), a field programmable gate array(FPGA), etc.

It is further noted that any process descriptions or blocks in flowcharts described above may represent modules, segments, and/or portionsof a computer program or application code that includes one or moreexecutable instructions for implementing specific logical functions orsteps in the process. Alternate implementations are included within thescope of the present invention in which functions may be executed out oforder from that shown in the figures and/or discussed above, includingsubstantially concurrently or in reverse order, depending at least inpart on the functionality involved, as will be understood by thoseskilled in the art.

With regard to any block diagrams described above, although the flow ofdata or other elements may be depicted as unidirectional orbi-directional, such depictions are merely exemplary and not limiting.Variations of the flows depicted in the block diagrams are includedwithin the scope of the present invention. Furthermore, thefunctionality of some of the blocks may be implemented by a singlecombined block within the scope of the present invention.

Moreover, embodiments of the present invention, such as those describedabove, may comprise an ordered listing of executable instructions forimplementing logical functions which can be embodied in anycomputer-readable medium for use by or in connection with an instructionexecution system, apparatus, or device, such as a computer-based system,processor-containing system, or other system that can fetch theinstructions from the instruction execution system, apparatus, or deviceand execute the instructions. In the context of this disclosure, a“computer-readable medium” may be any means that can contain, store,communicate, propagate, or transport the program for use by or inconnection with the instruction execution system, apparatus, or device.The computer readable medium may be, for example but not limited to, anelectronic, magnetic, optical, electromagnetic, infrared, orsemiconductor system, apparatus, device, or propagation medium. Morespecific examples (i.e., a non-exhaustive list) of the computer-readablemedium include the following: an electrical connection (electronic)having one or more wires, a portable computer diskette (magnetic), arandom access memory (RAM) (electronic), a read-only memory (ROM)(electronic), an erasable programmable read-only memory (EPROM or Flashmemory) (electronic), an optical fiber (optical), and a portable compactdisc read-only memory (CDROM) (optical). It is noted that thecomputer-readable medium may even be paper or another suitable mediumupon which the program is printed, as the program can be electronicallycaptured, via for instance optical scanning of the paper or othermedium, then compiled, interpreted or otherwise processed in a suitablemanner if necessary, and then stored in a computer memory.

Finally, it should be emphasized that the above-described embodiments ofthe present invention are merely possible examples of implementationsset forth for a clear understanding of the principles of the invention.Many variations and modifications may be made to the above-describedembodiment(s) of the invention without departing substantially from thespirit and principles of the invention. All such modifications andvariations are intended to be included herein within the scope of thisdisclosure and the invention, and protected by the following claims.

1. A computer program embodied in a computer readable medium forproviding efficient space-time structures for preambles, pilots and datafor multi-input, multi-output communications systems, the computerprogram comprising: logic configured to provide an initial structure;logic configured to verify that rows of said initial structure arelinearly independent; logic configured to apply an orthonormalizationprocedure to said initial structure to obtain a space-time structure fora preamble or pilot in a time or frequency domain; and logic configuredto insert the space-time structure as a preamble or pilot in the time orfrequency domain with one or more data symbols for transmission in themulti-input, multi-output communications system.
 2. The computer programof claim 1, wherein said logic configured to provide an initialstructure comprises: logic configured to choose a symbol alphabet toprovide symbols for said initial structure; and logic configured tochoose an initial configuration of said initial structure.
 3. Thecomputer program of claim 1, further comprising: logic configured toconfirm that symbols of said space-time structure are within apredetermined distance of symbols of said initial structure; logicconfigured to construct a space-time sequence structure from a pluralityof said space-time structures; and logic configured to verify that apeak-to-average power ratio of said space-time structure is less than apredetermined value.
 4. The computer program of claim 3, wherein saidlogic configured to confirm chat the symbols of said space-timestructure are within a predetermined distance of the symbols of saidinitial structure comprises logic configured to apply a Euclideandistance metric to determine the distance between the symbols of saidspace-time structure and the symbols of said initial structure.
 5. Thecomputer program of claim 1, wherein said logic configured to verifythat the rows of said initial structure are linearly independentcomprises logic configured to determine rank of said initial structure.6. The computer program of claim 1, wherein said logic configured toapply an orthonormalization procedure to said initial structure toobtain a space-time structure comprises logic configured to apply arow-wise Gram-Schmidt procedure to said initial structure to obtain aspace-time structure.